A positive displacement compressor takes in gas, compresses and thereby heats the gas and discharges the heated, pressurized gas in a pulsed discharge. The noise associated with a pulsed discharge is normally attenuated by a muffler. Because the speed of sound is dependent upon the temperature, the amount of entrained oil, and density of the medium through which it is traveling, in the case of a refrigerant compressor, ambient temperature and system loading will influence the speed of sound in the discharge gas. Further, variable speed operation will change the frequency of the pulses and unloading may decrease the discharge pressure and may produce changes in the discharge temperature depending upon the nature of the unloading. Because of the inherent fluctuation in temperature, density and pressure of the discharged gas and the frequency of the discharge pulses, a muffler would normally be acting on the gas at off-design conditions. Accordingly, the sound attenuation is normally less than that achieved at design conditions.
Reactive mufflers are called reactive not because they "react", but because their acoustic impedance is primarily reactive, as opposed to dissipative, that is, they absorb very little energy; instead, they work by reflecting the acoustic energy back toward the source. The electrical analogy is a filter circuit, which passes some frequencies and blocks others. Ideally, it is desirable to have a muffler which passes a frequency of zero (the steady flow) and blocks all other frequencies 100%. The problem is, this would require an infinitely large muffler with an infinite number of elements; thus, such a muffler would be impractical for size reasons as well as because of the cost.
As a result, one normally picks some reasonable number of elements and chooses their dimensions as a best compromise, considering the frequencies that are present to be attenuated (blocked). This solution always has certain "pass bands", i.e., frequencies ranges where energy is passed essentially unattenuated. The design skill is to pick the dimensions so these pass bands are at frequencies where the source machine has little or no energy generated.
Specifically, in HVAC positive displacement compression systems, there has traditionally been one advantage and one disadvantage compared to, say, internal combustion engine mufflers which are most commonly described in the literature. The advantage is that the compressors have been essentially constant speed, so the frequencies to be attenuated do not change much; the disadvantage is that most refrigerants are very dense and somewhat viscous at discharge conditions, so that any restrictions tend to cause large pressure drops and attendant losses in system efficiency. The compromise that has evolved is, typically, a 2 or 3 chamber muffler with re-entrant interconnecting tube(s).
The problem with this traditional approach on screw compressors as they are developing today (and to a lesser extent, other compressor technologies) is twofold: the machines will be applied variable speed, so the frequencies will vary over a broad range; and, they have a large and somewhat variable oil concentration, which changes the speed of sound in the discharge gas (having the same effect as a frequency change vis-a-vis muffler design). Trying to meet this challenge in muffler design traditionally leads to an excessively elaborate muffler with unacceptable pressure drop (i.e., efficiency loss).